516 research outputs found
A turning point analysis of the ergodic dynamics of iterative maps
The dynamics of one dimensional iterative maps in the regime of fully
developed chaos is studied in detail. Motivated by the observation of dynamical
structures around the unstable fixed point we introduce the geometrical concept
of a turning point which represents a local minimum or maximum of the
trajectory. Following we investigate the highly organized and structured
distribution of turning points. The turning point dynamics is discussed and the
corresponding turning point map which possesses an appealing asymptotic scaling
property is investigated. Strong correlations are shown to exist for the
turning point trajectories which contain the information of the fixed points as
well as the stability coefficients of the dynamical system. For the more
specialized case of symmetric maps which possess a symmetric density we derive
universal statistical properties of the corresponding turning point dynamics.
Using the turning point concept we finally develop a method for the analysis of
(one dimensional) time series.Comment: 37 pages, 11 figures, LaTeX, tccite.sty, to be published in the Int.
J. Bif. Chao
The beryllium atom and beryllium positive ion in strong magnetic fields
The ground and a few excited states of the beryllium atom in external uniform
magnetic fields are calculated by means of our 2D mesh Hartree-Fock method for
field strengths ranging from zero up to 2.35*10^9T. With changing field
strength the ground state of the Be atom undergoes three transitions involving
four different electronic configurations which belong to three groups with
different spin projections S_z=0,-1,-2. For weak fields the ground state
configuration arises from the 1s^2 2s^2, S_z=0 configuration. With increasing
field strength the ground state evolves into the two S_z=-1 configurations
1s^22s 2p_{-1} and 1s^2 2p_{-1}3d_{-2}, followed by the fully spin polarised
S_z=-2 configuration 1s2p_{-1}3d_{-2}4f_{-3}. The latter configuration forms
the ground state of the beryllium atom in the high field regime \gamma>4.567.
The analogous calculations for the Be^+ ion provide the sequence of the three
following ground state configurations: 1s^22s and 1s^22p_{-1} (S_z=-1/2) and
1s2p_{-1}3d_{-2} (S_z=-3/2).Comment: 15 pages, 7 figure
Many-Body Expansion Dynamics of a Bose-Fermi Mixture Confined in an Optical Lattice
We unravel the correlated non-equilibrium dynamics of a mass balanced
Bose-Fermi mixture in a one-dimensional optical lattice upon quenching an
imposed harmonic trap from strong to weak confinement. Regarding the system's
ground state, the competition between the inter and intraspecies interaction
strength gives rise to the immiscible and miscible phases characterized by
negligible and complete overlap of the constituting atomic clouds respectively.
The resulting dynamical response depends strongly on the initial phase and
consists of an expansion of each cloud and an interwell tunneling dynamics. For
varying quench amplitude and referring to a fixed phase a multitude of response
regimes is unveiled, being richer within the immiscible phase, which are
described by distinct expansion strengths and tunneling channels.Comment: 13 pages, 7 figure
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